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This book dwells on mathematical and algorithmic issues of data analysis based on generality order of descriptions and respective precision. To speak of these topics correctly, we have to go some way getting acquainted with the important…

Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and…

Topological data analysis (TDA) is a tool from data science and mathematics that is beginning to make waves in environmental science. In this work, we seek to provide an intuitive and understandable introduction to a tool from TDA that is…

We present Soda (Symbolic Objective Descriptive Analysis), a language that helps to treat qualities and quantities in a natural way and greatly simplifies the task of checking their correctness. We present key properties for the language…

Topological Data Analysis (TDA) can broadly be described as a collection of data analysis methods that find structure in data. This includes: clustering, manifold estimation, nonlinear dimension reduction, mode estimation, ridge estimation…

Object data analysis is concerned with statistical methodology for datasets whose elements reside in an arbitrary, unspecified metric space. In this work we propose the object shape, a novel measure of shape/symmetry for object data. The…

One of the purposes of Big Data systems is to support analysis of data gathered from heterogeneous data sources. Since data warehouses have been used for several decades to achieve the same goal, they could be leveraged also to provide…

Classification of ordinal data is one of the most important tasks of relation learning. In this thesis a novel framework for ordered classes is proposed. The technique reduces the problem of classifying ordered classes to the standard…

Training large neural networks on large-scale datasets requires substantial computational resources, particularly for dense prediction tasks such as object detection. Although dataset distillation (DD) has been proposed to alleviate these…

One of the main challenges for biomedical research lies in the computer-assisted integrative study of large and increasingly complex combinations of data in order to understand molecular mechanisms. The preservation of the materials and…

Deep learning approaches to object detection have achieved reliable detection of specific object classes in images. However, extending a model's detection capability to new object classes requires large amounts of annotated training data,…

Topological Data Analysis (TDA) is a rigorous framework that borrows techniques from geometric and algebraic topology, category theory, and combinatorics in order to study the "shape" of such complex high-dimensional data. Research in this…

Partial Wave Analysis has traditionally been carried out using a set of tools handcrafted for each experiment. By taking an object-oriented approach, the design presented in this paper attempts to create a more generally useful, and easily…

In a world abundant with diverse data arising from complex acquisition techniques, there is a growing need for new data analysis methods. In this paper we focus on high-dimensional data that are organized into several hierarchical datasets.…

Object detection and localization are crucial tasks for biomedical image analysis, particularly in the field of hematology where the detection and recognition of blood cells are essential for diagnosis and treatment decisions. While…

Topological Data Analysis (TDA) is a recent approach to analyze data sets from the perspective of their topological structure. Its use for time series data has been limited to the field of financial time series primarily and as a method for…

As edge devices become increasingly powerful, data analytics are gradually moving from a centralized to a decentralized regime where edge compute resources are exploited to process more of the data locally. This regime of analytics is…

Scientists use a mathematical subject called 'topology' to study the shapes of objects. An important part of topology is counting the numbers of pieces and holes in objects, and people use this information to group objects into different…

A central challenge in science is to understand how systems behaviors emerge from complex networks. This often requires aggregating, reusing, and integrating heterogeneous information. Supplementary spreadsheets to articles are a key data…

In a world increasingly awash with data, the need to extract meaningful insights from data has never been more crucial. Functional Data Analysis (FDA) goes beyond traditional data points, treating data as dynamic, continuous functions,…